Pertanyaan

Jika 9 x 2 − 6 x + 1 dan ( f ∘ g ) ( x ) = 9 x 2 + 6 x + 1 , maka g ( x − 3 2 ) = ....

Jika $9 x^{2} - 6 x + 1$ dan $(f \circ g) (x) = 9 x^{2} + 6 x + 1$ , maka $g (x - \frac{2}{3}) =$ ....

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Untuk memperoleh , maka substitusikan : Jadi, jawaban yang tepat adalah D.

$begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals 9 x squared plus 6 x plus 1 f open parentheses g open parentheses x close parentheses close parentheses equals 9 x squared plus 6 x plus 1 9 open parentheses g open parentheses x close parentheses close parentheses squared minus 6 x plus 1 equals 9 x squared plus 6 x plus 1 space space left parenthesis r u a s space k i r i space d i f a k t o r k a n right parenthesis I n g a t colon space left parenthesis a minus b right parenthesis squared equals a squared minus 2 a b plus b squared right parenthesis open parentheses 3 g open parentheses x close parentheses minus 1 close parentheses squared equals 9 x squared plus 6 x plus 1 3 g left parenthesis x right parenthesis minus 1 equals square root of 9 x squared plus 6 x plus 1 end root 3 g left parenthesis x right parenthesis minus 1 plus 1 equals square root of 9 x squared plus 6 x plus 1 end root plus 1 3 g left parenthesis x right parenthesis equals square root of 9 x squared plus 6 x plus 1 end root plus 1 space left parenthesis k e d u a space r u a s space d i b a g i space 3 right parenthesis g left parenthesis x right parenthesis equals fraction numerator square root of 9 x squared plus 6 x plus 1 end root plus 1 over denominator 3 end fraction end style$

Untuk memperoleh , maka substitusikan :

$begin mathsize 14px style g open parentheses x minus 2 over 3 close parentheses equals fraction numerator square root of 9 open parentheses x minus 2 over 3 close parentheses squared plus 6 open parentheses x minus 2 over 3 close parentheses plus 1 end root plus 1 over denominator 3 end fraction g open parentheses x minus 2 over 3 close parentheses equals fraction numerator square root of 9 open parentheses x squared minus 4 over 3 x plus begin display style 4 over 9 end style close parentheses plus 6 x minus 4 plus 1 end root plus 1 over denominator 3 end fraction g open parentheses x minus 2 over 3 close parentheses equals fraction numerator square root of 9 x squared minus 12 x plus begin display style 4 end style plus 6 x minus 3 end root plus 1 over denominator 3 end fraction g open parentheses x minus 2 over 3 close parentheses equals fraction numerator square root of 9 x squared minus 6 x plus begin display style 1 end style end root plus 1 over denominator 3 end fraction g open parentheses x minus 2 over 3 close parentheses equals fraction numerator square root of left parenthesis 3 x minus 1 right parenthesis squared end root plus 1 over denominator 3 end fraction g open parentheses x minus 2 over 3 close parentheses equals fraction numerator 3 x minus 1 plus 1 over denominator 3 end fraction g open parentheses x minus 2 over 3 close parentheses equals fraction numerator 3 x over denominator 3 end fraction g open parentheses x minus 2 over 3 close parentheses equals x end style$

Jadi, jawaban yang tepat adalah D.

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